# Math Help - Kinematics

1. ## Kinematics

A car traveling at a constant speed of 33.2m/s passes a trooper hidden behind a billboard at t = -1s. One second later, at t=0, the trooper sets in chase after the car with a constant acceleration of 2.92 m/s/s.

At what time t does the trooper overtake the speeding car? Answer in units of s.

For answers I tried 11.39683s and 22.739726s and both were wrong

2. Originally Posted by vesperka
A car traveling at a constant speed of 33.2m/s passes a trooper hidden behind a billboard at t = -1s. One second later, at t=0, the trooper sets in chase after the car with a constant acceleration of 2.92 m/s/s.

At what time t does the trooper overtake the speeding car? Answer in units of s.

For answers I tried 11.39683s and 22.739726s and both were wrong
Let's simply start our clock at t = 0 s. I am using a coordinate system where the origin is the point where the car and cop are at t = 0 s, and choose the +x direction in the direction of the velocity of the car.

So for the car:
$x_0 = 0~m$
$v_0 = 33.2~m/s$ <-- This is constant.
$a = 0~m/s^2$

The position of the car is given as
$x = x_0 + v_0t = 33.2t$

For the cop:
$x_0 = 0~m$
$v_0 = 0~m/s$
$a = 2.92~m/s^2$

The position of the cop is given as
$x = x_0 + v_0t + \frac{1}{2}at^2 = 1.46t^2$

We want to find where the car and cop meet, so equate these two expressions:
$x = 33.2t = 1.46t^2$

Now solve for t.
I get $t = 0~s$ (which we already knew) and $t = 22.7397~s$

It is possible that the computer didn't accept your second (and correct) answer because you didn't give the result to the proper number of significant digits: t = 22.7 s.

-Dan

3. Hmm, I tried 22.7 also and it's still no good. I'll e-mail my teacher and see what he has to say on the issue, this is weird

4. Originally Posted by vesperka
Hmm, I tried 22.7 also and it's still no good. I'll e-mail my teacher and see what he has to say on the issue, this is weird
I'm curious to see what your teacher has to say about it.

-Dan

5. He probably won't respond for a while, but I thought of something.

The position function of the car is:

33.2x+33.2

because at 0 seconds the car is 33.2 meters ahead. I can't come up with a valid position function for the police though. I'm having a bit of a brain block, it seems like there should be a way to find position at any given time knowing only acceleration.

Would the position function for the police be 1.46x^2 ?

From this, the velocity would be 2.92X and the acceleration would be 2.92, just like was given.

6. There we go

The position of the car is 33.2X + 33.2 and the position of the police is 1.46x^2.

Then I just found the intersection on the calculator and got 23.699239s as my answer and it worked. Thanks for helping me on this one

7. Ah! I just saw what I did wrong. The cop starts one second later.

Grrr... And I had consciously thought of that when I started writing the response and forgot it almost immediately. I hate it when that happens!

-Dan